Exam 15: Nonparametric Tests

As part of a large,ongoing diet study,some subjects of the study are taking part in an intensive exercise program for four weeks.Several variables are measured on these subjects,both at the beginning and at the end of the four-week period.Some of these variables are weight,cholesterol,and triglyceride level.One objective of this particular study is to assess the effect of diet and intense exercise on increasing triglyceride levels.The data for a simple random sample of nine of these subjects are given in the table below. The data are to be analyzed using the Wilcoxon signed rank test.Under the null hypothesis that triglyceride levels have the same distribution at the beginning and at the end of the study,what is the expected value of the test statistic W⁺?

Some researchers have conjectured that stem-pitting disease in peach-tree seedlings might be controlled with weed and soil treatment.An experiment was conducted to compare peach-tree seedling growth with soil and weeds treated with one of two herbicides.In a field containing twelve seedlings,six were randomly selected throughout the field and assigned to receive Herbicide A.The remaining six were to receive Herbicide B.Soil and weeds for each seedling were treated with the appropriate herbicide,and at the end of the study period the height in centimeters was recorded for each seedling.The following results were obtained. Let W be the Wilcoxon rank sum test statistic equal to the sum of the ranks assigned to the Herbicide A group.What is the expected value of W under the null hypothesis that the two distributions are the same?

At what age do babies learn to crawl? Does it take longer to learn in the winter when babies are often bundled in clothes that restrict their movement? Data were collected from parents who brought their babies into the University of Denver Infant Study Center to participate in one of a number of experiments between 1988 and 1991.Parents reported the birth month and the age at which their child was first able to creep or crawl a distance of 4 feet within 1 minute.The resulting data were grouped by month of birth: January,May,and September. The data are to be analyzed with the Kruskal-Wallis test.What is the value of the Kruskal-Wallis statistic H for these data?

The Wilcoxon rank sum test will accurately test the hypotheses H₀: median₁ = median₂ vs H_a: median₁ > median₂ as long as what additional assumption is met?

As part of a large,ongoing diet study,some subjects of the study are taking part in an intensive exercise program for four weeks.Several variables are measured on these subjects,both at the beginning and at the end of the four-week period.Some of these variables are weight,cholesterol,and triglyceride level.One objective of this particular study is to assess the effect of diet and intense exercise on increasing triglyceride levels.The data for a simple random sample of nine of these subjects are given in the table below. The data are to be analyzed using the Wilcoxon signed rank test.Arrange the ten observations in order and assign ranks.What rank does the difference of 6 receive?

A private university is trying to determine if there is pay equity among the male and female faculty.A simple random sample of six faculty members was selected from each gender group and the salary was recorded.The data (in thousands)are shown below. Rank all of the observations together.What is the list of ranks for the female group?

To use nonparametric methods,the distribution of the population should be ________.

"Cramming" is a technique often used by students to prepare for exams,in which they study for extended hours only a few days before the exams.Often students drink caffeinated beverages to help them stay awake while cramming for exams.Five students were randomly selected and asked to drink highly caffeinated beverages before their first midterm exam and then drink only water before their second midterm exam in the same subject.The difference of the scores (midterm 2 - midterm 1)is shown below for the five students. Using the normal approximation with the continuity correction,what is the P-value used to test the null hypothesis of no difference against the alternative hypothesis that midterm 2 scores are systematically higher than midterm 1 scores using the Wilcoxon signed rank test statistic?

Some researchers have conjectured that stem-pitting disease in peach-tree seedlings might be controlled with weed and soil treatment.An experiment was conducted to compare peach-tree seedling growth with soil and weeds treated with one of two herbicides.In a field containing twelve seedlings,six were randomly selected throughout the field and assigned to receive Herbicide A.The remaining six were to receive Herbicide B.Soil and weeds for each seedling were treated with the appropriate herbicide,and at the end of the study period the height in centimeters was recorded for each seedling.The following results were obtained. Let W be the Wilcoxon rank sum test statistic equal to the sum of the ranks assigned to the Herbicide A group.Using the Normal approximation,what is the value of the two-sided P-value for the test?

In a study to investigate the effect of diet on reducing cholesterol levels,a random sample of five subjects known to have high cholesterol had their cholesterol measured at the beginning of the study and after 6 months on a special diet.The data are given in the table below. The data are to be analyzed using the Wilcoxon signed rank test.What is the standardized value z of W⁺?

Does income increase when you get married? To investigate this,a college student has randomly selected people from his college town and collected income data for these people.They were categorized according to their marital status.The following results (in thousands of dollars)were obtained. The data are to be analyzed using the Wilcoxon rank sum test.Let W be the Wilcoxon rank sum test statistic equal to the sum of the ranks assigned to the married group.Using the Normal approximation with the continuity correction,what is the P-value for this test?

"Cramming" is a technique often used by students to prepare for exams,in which they study for extended hours only a few days before the exams.Often students drink caffeinated beverages to help them stay awake while cramming for exams.Five students were randomly selected and asked to drink highly caffeinated beverages before their first midterm exam and then drink only water before their second midterm exam in the same subject.The difference of the scores (midterm 2 - midterm 1)is shown below for the five students. What is the value of,W⁺,the Wilcoxon signed rank test statistic? (Note: Use the positive difference. )

When ranking observation from smallest to largest for use with the Wilcoxon rank sum test and there is a tie,it is best to ___________.

Which of the following statements about the Kruskal-Wallis test are FALSE?

Laureysens,et al.(2004)studied the concentration of aluminum in wood from a number of clones of poplar growing in an area with heavy pollution.The same clone was sampled and tested once in August and again in November.The researchers believed that the concentration of aluminum would be shown to be increasing over time and hence higher in November than in August.The following table gives the aluminum concentrations for twelve of the clones. The data are to be analyzed using the Wilcoxon signed rank test.The null hypothesis they established was that the values of aluminum concentrations in the 2 months have the same distribution.What is the value of the statistic W⁺ used for the test of hypotheses?

A researcher has determined that the data obtained in a small study are clearly not Normally distributed.If the researcher had hoped to make inferences based on the data,what might the researcher consider doing in this situation?

Some researchers have conjectured that stem-pitting disease in peach-tree seedlings might be controlled with weed and soil treatment.An experiment was conducted to compare peach-tree seedling growth with soil and weeds treated with one of two herbicides.In a field containing twelve seedlings,six were randomly selected throughout the field and assigned to receive Herbicide A.The remaining six were to receive Herbicide B.Soil and weeds for each seedling were treated with the appropriate herbicide,and at the end of the study period the height in centimeters was recorded for each seedling.The following results were obtained. When ranking all the observations together,what rank should be assigned to the observations with a height of 77 centimeters?

A private university is trying to determine if there is pay equity among the male and female faculty.A simple random sample of six faculty members was selected from each gender group and the salary was recorded.The data (in thousands)are shown below. Based on the Wilcoxon rank sum test,is there evidence that the male faculty make more money than the female faculty?

A private university is trying to determine if there is pay equity among the male and female faculty.A simple random sample of six faculty members was selected from each gender group and the salary was recorded.The data (in thousands)are shown below. Rank all the observations together.What is the list of ranks for the male group?

Does income increase when you get married? To investigate this,a college student has randomly selected people from his college town and collected income data for these people.They were categorized according to their marital status.The following results (in thousands of dollars)were obtained. The data are to be analyzed using the Wilcoxon rank sum test.Arrange the ten observations in order and assign ranks.What rank does the observation with an income of $116,000 receive?